A
28
o
B
3.0m m m
Physics 211: Mechanics
Final Review
Page 1 of 6
Summary of Equations, Constants, and Conversion Factors
Motion
=
v drdt
=
a dvdt
Linear Motion
=
+
+
r r0 v0t 12a0t2
=
+
v v0 at
=
+
v2 v02 2ar
Uniform Circular Motion
=
ac v2r
=
ac ω2r
=
T 2πrv
Rotational Motion
=
+
θ ω0t 12αt2
=
+
ω ω0 αt
=
+
ω2 ω02 2αθ
Simple Harmonic Motion
=
+
x Acosωt ϕ
=
(
+ )
v
ωA sin ωt ϕ
=
(
+ )
a
ω2A cos ωt ϕ
=
ω 2πf
=
f 1T
=±

v
ωA2 x2
=
a
ω2x
Wave Motion
( , )=
(

)
y x t
A sin kx ωt
=
k 2πλ
=
ω 2πT
=
v fλ
=
λn 2Ln
=
v FTμ
Pendulum Motion
Simple:
=
T 2πLg
Physical:
=
T 2πImgh
Linear Kinetics
=
P mv
=
F ma
=
F dPdt
=
fs μsFn
=
fk μkFn
=
D 12CρAv2
Rotational Kinetics
=
L Iω
= ×
l r P
=
⊥
τ rF
= ×
τ r F
=
τ dLdt
=
+
I Icom mh2
=
I mr2
Simple Harmonic Kinetics
=
F
kx
=
k ω2m
Elasticity
=
FA EΔLL
=
FA GΔxL
=
p BΔVV
Energy
=
+
+
+
E Ue Ug Kr Kt
=
Ue 12kx2
=
Ug mgh
=
Kr 12Iω2
=
Kt 12mv2
Work
=
=
=
w x0x1Fxdx Fr τθ
=
=
=
=
P dwdt dEdt Fv τω
=
+
=
wnet wnc wc ΔK
=
wc
ΔU
=
wnc ΔE
=
Fx
dUdx
Gravity
=
=
Fg W GmMR2
=
Ug
GmMR
Constants/Conversions
= .
×

G 6 67 10 11
= .
/
g 9 81 m s2
= . ×
/
c 3 0 108m s
=
1 rev 2π rad
=
.
1 hp 745 7 W
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View Full DocumentPhysics 211: Mechanics
Final Review
Page 2 of 6
Part I: Motion in One Dimension
1.
At a certain time a particle had a speed of 18 m/s in the positive x direction, and 2.4 s
later its speed was 30 m/s in the opposite direction. What is the average acceleration of
the particle during this 2.4 s interval?
Answer: 20 m/s
2
2.
A key falls from a bridge that is 45 m above the water. It falls directly into a model boat,
moving with constant velocity, that is 12 m from the point of impact when the key is
released. What is the speed of the boat?
Answer: 4.0 m/s
3.
A shuffleboard disk is accelerated at a constant rate from rest to a speed of 6.0 m/s over a
1.8 m distance by a player using a cue. At this point the disk loses contact with the cue
and slows at a constant rate of 2.5 m/s
2
until it stops. (a) How much time elapses from
when the disk begins to accelerate until it stops? (b) What total distance does the disk
travel?
Answer: (a) 3.0 s (b) 9.0 m
4.
A Chevy truck is cruising down the highway at a constant 66.0 f/s. At time t = 0 a BMW
moving at 144 f/s is 301 feet behind the truck. If at that instant the BMW starts to slow
down at a constant rate of magnitude 14.0 f/s
2
, at what time will the BMW be closest to
the Chevy? The Chevy’s velocity does not change.
Answer: 5.57 s
Part II: Motion in Two Dimensions
5.
A football player punts the football so that it will have a “hang time” (time of flight) of
4.5 s and land 46 m away. If the ball leaves the player’s foot 150 cm above the ground,
what must be the (a) magnitude and (b) angle (relative to the horizontal) of the ball’s
initial velocity?
Answer: (a) 24 m/s (b) 65°
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 Spring '08
 staff
 Physics, mechanics, Force, Friction, Mass, m/s

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